A New Way Of characterizing Surface Roughness

Girish Nathan, Gemunu H. Gunaratne
University of Houston

We propose a new diagnostic for characterizing rough surfaces. This parameter, called the disorder parameter, is based on the Hessian of the input field and is initial-configuration independent. The exact form of the parameter relies on rigid rotational and translational invariance. We identify a spectrum of moments that can be used to highlight low and high-curvature regions. In this paper, the method is applied to two recipes of interface growth, the Ballistic Deposition (BD) and the Restricted Solid-On-Solid (RSOS) models. It is shown that the behavior of the moments in time is similar to standard measures of surface roughness - that is, the interface width as a function of time. One can extract growth and roughness exponents from the disorder parameter to quantify the growth process. We then apply the method to the speckle pattern obtained from these growing interfaces and show that the moments obtained numerically are qualitatively similar to those obtained from analysis of the surface data. This is not always true for the usual correlation functions. Therefore, we propose that the disorder parameter might be a good suppelement to the correlation functions already being used extensively in the field.